An error 2% in excess is made while measuring the side of a square. The…
2025
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
- A.
406
- B.
404
- C.
102
- D.
106
Attempted by 178 students.
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Correct answer: B
Key idea: the area changes by the square of the linear scale factor.
Let the true side be s. A 2% excess makes the measured side = 1.02 × s.
True area = s². Measured area = (1.02 s)² = 1.0404 s².
Percentage error in area = (1.0404 − 1) × 100% = 4.04%.
Numeric check: If the true side = 100 cm, true area = 10000 cm². Measured side = 102 cm, measured area = 102² = 10404 cm². Increase = 404 cm², and 404/10000 × 100% = 4.04%.
Therefore the percentage error in the calculated area is 4.04%, which corresponds to the option text "404" (interpreted as 4.04%).